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Quasilinear Simulation of the Development of Weibel Turbulence in Anisotropic Collisionless Plasma

  • STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS
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Abstract

A spectral quasilinear approach to the problem of TEM-Weibel instability in an anisotropic collisionless plasma is developed, which takes into account only the integral nonlinear interaction of modes through the joint variation of the spatially averaged particle velocity distribution induced by these modes. Within this approximation, a closed system of equations is obtained for the one- and two-dimensional evolution of spatial modes (harmonics) of the distribution function of particles and the electromagnetic field under conditions when the plasma anisotropy axis, the wave vector, and the magnetic field of the modes are orthogonal to each other. The numerical solution of this system of equations is compared with the available results of one-dimensional analytical quasilinear theory in the region of its applicability, as well as with the results of two-dimensional simulation by the particle-in-cell method, which also takes into account the direct four-wave interaction of modes. It is established that in the simplest cases of one-dimensional and axially symmetric two-dimensional problems for a bi-Maxwellian plasma, quasilinear phenomena play the leading role at a quite long stage of nonlinear development of turbulence. It is noted that at a later stage of decay of turbulence and in a more general formulation of the problem, in particular, in the presence of an external magnetic field, the direct nonlinear interaction of modes can manifest itself along with quasilinear phenomena. Based on the analysis carried out, the contribution of certain nonlinear effects to the evolution of the spatial spectrum of Weibel turbulence is revealed, and the properties of this turbulence are studied, including the self-similar character and qualitatively different stages of the dynamics of unstable modes.

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Notes

  1. In many cases this relationship is slightly better satisfied by the wave number Kmax(t) corresponding to the maximum of the turbulence spectrum, rather than the above number 〈K〉 averaged over the mode spectrum bk, although these numbers are close enough.

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ACKNOWLEDGMENTS

Numerical calculations were performed using the supercomputer resources of the Center for Collective Use of the Keldysh Institute of Applied Mathematics, Russian Academy of Sciences.

Funding

The calculations of the dynamics of Weibel modes within the framework of one-dimensional problem were supported by the Russian Science Foundation (project no. 19-72-10111). The calculation of the evolution of the spectrum in axially symmetric two-dimensional problem was supported by the Theoretical Physics and Mathematics Advancement Foundation “BASIS” (project no. 20-1-1-37-2).

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Authors and Affiliations

  1. Institute of Applied Physics, Russian Academy of Sciences, 603950, Nizhny Novgorod, Russia

    A. A. Kuznetsov, A. A. Nechaev, M. A. Garasev & Vl. V. Kocharovsky

Authors
  1. A. A. Kuznetsov
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  2. A. A. Nechaev
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  3. M. A. Garasev
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  4. Vl. V. Kocharovsky
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Correspondence to A. A. Kuznetsov.

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Translated by I. Nikitin

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Kuznetsov, A.A., Nechaev, A.A., Garasev, M.A. et al. Quasilinear Simulation of the Development of Weibel Turbulence in Anisotropic Collisionless Plasma. J. Exp. Theor. Phys. 137, 966–985 (2023). https://doi.org/10.1134/S1063776123120099

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  • DOI: https://doi.org/10.1134/S1063776123120099

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